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To calculate the RMSE (Root Mean Squared Error), we follow these steps:

1. **Identify the observed values (Time Series Value) and the predicted values (Forecast)**.
   - Observed values: \(6, 3, 5, 2, 8\)
   - Forecast values: \(6.00, 6.00, 3.00, 7.00, 7.00\)

2. **Calculate the squared differences for each pair**:
   \[
   \text{Squared Differences} = (Observed - Forecast)^2
   \]

3. **Find the mean of these squared differences**.

4. **Take the square root of that mean** to get the RMSE.

Let's calculate it step-by-step.The RMSE (Root Mean Squared Error) for the given data is **2.79**.

Would you like more details or have any questions about this calculation?

Here are 5 related questions to deepen your understanding:

1. What is the difference between RMSE and Mean Absolute Error (MAE)?
2. How can RMSE be used to evaluate the accuracy of forecasting models?
3. Why is RMSE sensitive to outliers, and how does this affect its interpretation?
4. Can RMSE be used for comparing models with different scales of data?
5. How do you interpret RMSE in real-world applications?

**Tip:** RMSE is particularly useful when large errors are more undesirable than smaller ones, as it emphasizes larger deviations due to the squaring process.

Using the data below, what is the value of RMSE?

Learn how to calculate RMSE (Root Mean Squared Error) for a given time series data set. Example data includes observed values: 6, 3, 5, 2, 8, and forecast values: 6.00, 6.00, 3.00, 7.00, 7.00. Suitable for high school and college-level students studying statistics or forecasting models.

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